function [empirical_cov_list, rcv_cell] = ecf_over_nu_robust(hat_theta, rep_base_se2, hat_vartheta, rep_val_se2, meta_nu_list)
%INPUT: baseline and validation study data, list of meta analyst's nu
%OUTPUT: empirical coverage frequencies evaluated at each nu in meta_nu_list, 
% table of reobust critical values for each nu
    
    % Initialization
    K = size(meta_nu_list, 2);
    empirical_cov_list = zeros(1, K);
    rcv_cell = cell(K, 1);

    for k = 1:length(meta_nu_list)
        % Set the value of meta analyst's nu
        meta_nu = meta_nu_list(k);
            
        % Check whether the validation study estimates are located in the predicted interval
        [empirical_cov, rcv_table] = check_CI_over_nu_robust(hat_theta, hat_vartheta, rep_base_se2, rep_val_se2, meta_nu);
    
        % Store the results
        empirical_cov_list(1, k) = empirical_cov;
        rcv_cell{k} = rcv_table;

    end
end